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Simplifying 3p2 + -18p + -4 = 0 Reorder the terms: -4 + -18p + 3p2 = 0 Solving -4 + -18p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -6p + p2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -6p + 1.333333333 + p2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -6p + p2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -6p + p2 = 0 + 1.333333333 -6p + p2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -6p + p2 = 1.333333333 The p term is -6p. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6p + 9 + p2 = 1.333333333 + 9 Reorder the terms: 9 + -6p + p2 = 1.333333333 + 9 Combine like terms: 1.333333333 + 9 = 10.333333333 9 + -6p + p2 = 10.333333333 Factor a perfect square on the left side: (p + -3)(p + -3) = 10.333333333 Calculate the square root of the right side: 3.214550254 Break this problem into two subproblems by setting (p + -3) equal to 3.214550254 and -3.214550254.Subproblem 1
p + -3 = 3.214550254 Simplifying p + -3 = 3.214550254 Reorder the terms: -3 + p = 3.214550254 Solving -3 + p = 3.214550254 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 3.214550254 + 3 Combine like terms: -3 + 3 = 0 0 + p = 3.214550254 + 3 p = 3.214550254 + 3 Combine like terms: 3.214550254 + 3 = 6.214550254 p = 6.214550254 Simplifying p = 6.214550254Subproblem 2
p + -3 = -3.214550254 Simplifying p + -3 = -3.214550254 Reorder the terms: -3 + p = -3.214550254 Solving -3 + p = -3.214550254 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -3.214550254 + 3 Combine like terms: -3 + 3 = 0 0 + p = -3.214550254 + 3 p = -3.214550254 + 3 Combine like terms: -3.214550254 + 3 = -0.214550254 p = -0.214550254 Simplifying p = -0.214550254Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.214550254, -0.214550254}
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